Multiple Length and/or Time Scales
The papers listed below address problems with multiple length and/or time scales. Applications include short wave scattering, multiphase mechanics problems, analysis of complex structures, and waves in heterogeneous media. The approaches used vary depending upon the particular application, but almost invariably involve asymptotic analysis. The hybrid asymptotic-numerical methods described in the papers below show how to couple field equations describing phenomena on different scales.

Relevant papers on multiple scales
  1. “Coupling between elastic strain and interstitial fluid flow: Ramifications for poroelastic imaging,” R Leiderman, PE Barbone, AA Oberai, JC Bamber. Physics in Medicine and Biology, 51 (24), pp. 6291-6313, 2006. Included in Highlights of 2006 .
  2. “Multiple length and time scales in acoustics,” Paul E. Barbone, Aerotecnica Missili e Spazio, 79(3-4):65–74, 2000.
  3. “Canonical representations of complex vibratory subsystems: Time domain Dirichlet to Neumann maps,” Paul E. Barbone, Aravind Cherukuri and Daniel Goldman, Internat. J. of Solids and Struct., vol. 37, pp. 2825–2857, 2000.
  4. “A Phase-Plane Description of Nonlinear Traveling Waves in Bubbly Liquids,” A. Nadim, D. Goldman, J.J. Cartmell and Paul E. Barbone, Journal of Computational Acoustics, Vol 7(2), pp. 71-82, June 1999.
  5. “Scattering from submerged objects by a hybrid asymptotic-boundary integral equation method,” Paul E. Barbone and Ofer Michael, Wave Motion, Vol 29, pp. 137–156, 1999.
  6. “Scattering by a Hybrid Asymptotic/Finite Element Method,” Paul E. Barbone, Joshua M. Montgomery, Ofer E. Michael and Isaac Harari, Computer Methods in Applied Mechanics and Engineering, Vol. 164, Nos. 1-2, pp. 141–156, October 1998.
  7. “High Modal Density Approximations for Equipment in the Time Domain,” Aravind Cherukuri and Paul E. Barbone. Journal of the Acoustical Society of America, vol 104(4), pp. 2048-2053, October 1998.
  8. “Diffraction from simple shapes by a hybrid asymptotic-numerical method,” Joshua M. Montgomery and Paul E. Barbone, Journal of the Acoustical Society of America, vol 104(4), pp. 1964–1972, October 1998.
  9. “Finite Element Formulations for Exterior Problems: Application to Hybrid Methods, Non-reflecting Boundary Conditions, and Infinite Elements,” Isaac Harari, Paul E. Barbone and Joshua M. Montgomery, International Journal for Numerical Methods in Engineering, Vol. 40, 1997, pp. 2791–2805.
  10. “Approximate Diffraction Coefficients by the Method of Matched Asymptotic Expansions,” Paul E. Barbone, Wave Motion, Vol. 22, pp. 1-16, 1995.
  11. “Stability of Harmonic Waves in a Periodic System and the Radiation Condition,” Paul E. Barbone, ASME Journal of Applied Mechanics, Vol. 61, No. 4, pp. 980–983, 1994.
  12. “Disorder and Localization in Ribbed Structures with Fluid Loading,” M. Spivack & Paul E. Barbone, Proc. R. Soc. Lond. A, vol. 444, 73-89, 1994.
  13. “Effective Dynamical Properties,” Paul E. Barbone, Proc. ASME Noise Control and Acoustics Division, No. G0 1089, 1998 International Mechanical Engineering Congress, Anaheim, CA, November 15–20, 1998. ASME Press, New York, pg. 333–339.
  14. “Dirichlet to Neumann Maps for the Representation of Equipment with Weak Nonlinearities,” Daniel Goldman and Paul E. Barbone, Proc. ASME Noise Control and Acoustics Division, Vol. NCA22, pp. 71–76, Proceedings of the 1996 International Mechanical Engineering Congress, Atlanta, GA, November 17–22, 1996.
  15. “Equipment Representations for Shock Calculations: Time Domain Dirichlet to Neumann Maps,” Paul E. Barbone, BU Dept. Aerospace & Mechanical Engineering Technical Report No. AM-95-012, also in Acoustics, Vibrations, and Rotating Machines, Vol. 3, Part B, pp. 223–228, Proceedings of the 1995 Design Engineering Technical Conferences, Sept. 17–20, 1995. ASME Press, New York.
  16. “Forward and Inverse Scattering in Media with Microstructure,” Rebecca B. Shuman and Paul E. Barbone, BU Dept. Aerospace & Mechanical Eng. Technical Report No. AM-98-025, May 1998.
  17. “Pressure-density relation and acoustics in bubbly liquids,” Ali Nadim, Paul E. Barbone, and Daniel Goldman, BU Dept. Aerospace & Mechanical Engineering Technical Report No. AM-95-008.
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